{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ade9f831",
   "metadata": {},
   "source": [
    "# 项目1：不动点迭代法"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2e28d9b",
   "metadata": {},
   "source": [
    "## 这里作封面待定图\n",
    "<img src=\"Cover1.png\" width = \"500\" height = \"500\" alt=\"image\" align = center/>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b6eb1aa",
   "metadata": {},
   "source": [
    "## 1.迭代公式的推导\n",
    "由$x ^ 2 = 2$\n",
    "\n",
    "$2x^ 2 = x ^ 2 + 2 $\n",
    "\n",
    "$\\frac {2x^2}{2x} = \\frac{2+x}{2x}+\\frac{x^2}{2x}$\n",
    "\n",
    "$x = \\frac{1}{x}+\\frac{x}{2}$\n",
    "\n",
    "迭代公式由此即得"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f148ce2",
   "metadata": {},
   "source": [
    "## 2.迭代公式的实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "d91542a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np  #用numpy来帮助实现迭代公式\n",
    "def calXnew(Xold):\n",
    "    return(1/Xold)+(Xold/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e7cc3372",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i: 0  Xold: 10  Xnew: 5.1  Diff: 4.9\n",
      "i: 1  Xold: 5.1  Xnew: 2.746078431372549  Diff: 2.3539215686274506\n",
      "i: 2  Xold: 2.746078431372549  Xnew: 1.7371948743795984  Diff: 1.0088835569929506\n",
      "i: 3  Xold: 1.7371948743795984  Xnew: 1.4442380948662321  Diff: 0.2929567795133663\n",
      "i: 4  Xold: 1.4442380948662321  Xnew: 1.4145256551487377  Diff: 0.029712439717494377\n",
      "i: 5  Xold: 1.4145256551487377  Xnew: 1.4142135968022693  Diff: 0.00031205834646841346\n",
      "i: 6  Xold: 1.4142135968022693  Xnew: 1.4142135623730954  Diff: 3.442917395624079e-08\n",
      "finished the result is  1.4142135623730954\n"
     ]
    }
   ],
   "source": [
    "#该模块在代码上实现迭代公式\n",
    "Xold = 10                    #设定要进行迭代的初始数值\n",
    "error = 1e-4                 #设定好误差\n",
    "i = 0                        #设置i为迭代次数的计数器\n",
    "maxIter = 50                 #设置一个迭代次数的最大值，i如若超过此值则强制结束迭代 \n",
    "listXnew = []                #这里将Xnew,Xold,i和difference存入list中，便于后续做图\n",
    "listXold= []\n",
    "list_i = []\n",
    "listdiff = []\n",
    "\n",
    "while(i < maxIter):\n",
    "    Xnew = calXnew(Xold)\n",
    "    difference = abs(Xnew - Xold)\n",
    "    listXnew.append(Xnew)    \n",
    "    list_i.append(i)\n",
    "    listdiff.append(difference)\n",
    "    listXold.append(Xold)\n",
    "    \n",
    "    print(\"i:\",i,\" Xold:\",Xold,\" Xnew:\",Xnew,\" Diff:\",difference)\n",
    "    if difference < error:\n",
    "        print(\"finished the result is \",Xnew)\n",
    "        break  \n",
    "             \n",
    "    Xold = Xnew\n",
    "    i += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4f488458",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt  #使用matplotlib做图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "308d3ca2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Xnew')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list_i,listXnew)\n",
    "plt.xlabel(\"i\",fontsize = 20)\n",
    "plt.ylabel(\"Xnew\",fontsize = 18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cdb51ae0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Difference')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(list_i,listdiff)\n",
    "plt.xlabel(\"i\",fontsize = 20)\n",
    "plt.ylabel(\"Difference\",fontsize = 18)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a8daad0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Xnew')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(listXold,listXnew)\n",
    "plt.xlabel(\"Xold\",fontsize = 20)\n",
    "plt.ylabel(\"Xnew\",fontsize = 18)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
